Whether it be economical or the reverse to use for bridge construction any particular alloy of steel instead of standard carbon steel will depend upon three fundamental conditions, viz.,

A. The ratio of costs per pound erected of carbon steel and the       alloy steel under consideration.

B. The ratio of the elastic limits of these two steels.

C. The type and the span length, or span lengths, of the structure       contemplated.

If r (greater than unity) is the ratio of costs per pound erected of the alloy steel and carbon steel, and r' (less than unity) is the ratio of elastic limits of the two metals, then for primary truss members of rods or bars the economy in using the alloy will depend upon whether the product of r and r' is less than unity, or mathematically

This criterion will not hold good for spans; because, while the ratio of intensities of working stresses for simple (unstiffened) tension members of untreated steel † is exactly equal to that of the elastic limits, the varying ratios of the intensities of working stresses for compression members and for rigid tension members (on gross sections) differ materially therefrom. Moreover, a certain portion of the weight of metal in a structure is not affected by varying the intensities of working stresses. Again, the criterion would take no cognizance of the reduction of dead load due to the smaller weight of steel involved by using the alloy. The first and second of the variations mentioned are of opposite sign from the third, and, in consequence, the tendency of the combination is to offset; but the preponderance,  except  in  the  case  of  unusually  long  spans,  is in favor of the

* After this chapter was completed, its contents were used as a basis for a paper presented to the Académie des Sciences of France, entitled "L'Émploi Économique des Alliages d'Acier pour la Construction des Ponts," all quantities in both diagrams and text being changed to French units. The paper was published in condensed form by the Academy on July 12, 1920, and in full by Le Génie Civil on July 24, 1920.

† In the case of eye-bars of treated steel, the intensity of working tensile stress is taken as either one-half of the elastic limit or one-third of the ultimate strength—whichever of the two is the smaller.

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